-6(3/4x-2)+3=1/2x+7

Solution for -6(3/4x-2)+3=1/2x+7 equation:

-6(3/4x-2)+3=1/2x+7

We move all terms to the left:

-6(3/4x-2)+3-(1/2x+7)=0


Domain of the equation: 4x-2)!=0

x∈R



Domain of the equation: 2x+7)!=0

x∈R


We multiply parentheses

-18x-(1/2x+7)+12+3=0

We get rid of parentheses

-18x-1/2x-7+12+3=0

We multiply all the terms by the denominator


-18x*2x-7*2x+12*2x+3*2x-1=0

Wy multiply elements

-36x^2-14x+24x+6x-1=0

We add all the numbers together, and all the variables

-36x^2+16x-1=0

a = -36; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·(-36)·(-1)
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{7}}{2*-36}=\frac{-16-4\sqrt{7}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{7}}{2*-36}=\frac{-16+4\sqrt{7}}{-72}
$